Dave,
The songs you have listed above are rarities indeed. Going by your definition of songs that have been played 10 times or less during their career, I can think of:

1. We're An American Band
2. Lean On Me
3. Homebound Train ???
4. You Had Me From Hello
5. Fields of Fire
6. Good Guys Don't Always Wear White
7. Lie To Me
8. Back in the USSR
9. Stick To Your Guns

I'd say about half of the rarities according to your list and mine are covers and not Bon Jovi songs...


My Take on it:
The problem is that when you look at the Bounce Tour, the Have a Nice Day Tour and Lost Highway tours, for the most part, the setlists were very stagnant. When they did change, they were replaced with something that wasn't rare for example substituting "Captain Crash..." with "Radio....".

So having said that, I think the definition of a rairty changes from decade to decade or from tour to tour. For instance, song like "Hey God" which was played frequently in 1995-1996, would be considered rare song now (at least to me) if it were to pop up in a setlist from the 2000s. According to Seb's site, since 2000 "Hey God" has only been played a total of 8 times (4 on LH tour). Furthermore since 2000, the band have been on 5 different "world tours" and only played the song 8 times amounting to a lousy average of 1.6 times a tour. I'd say that make s it pretty rare now...